You want a program with a good combination of clinical exposure, research, quality teaching, lifestyle, and potential future opportunities.
Take for example just the following:
Clinical exposure: the different types of rotations available:
- Emergency psychiatry
- PACT/ACT teams
- Inpatient: Voluntary and/or involuntary
- forensic psychiatry
- child psychiatry
- eating disorders
- ECT
- psychotherapy
- long term inpatient psychiatric facilities
- consult liason psychiatry
Several programs I've seen do not offer all the above. Where I did residency residents were split between two locations. At one we had all of the above except for long term units and an eating disorder clinic. At the other, they didn't have PACT/ACT teams, involuntary inpatient or emergency psychiatry. Trust me, if you didn't do one, you will not be prepared for it by the time you graduate.
We had a 4th year resident come over to the other location as an elective who never did involuntary inpatient. She didn't know how to fill out involuntary commitment forms. She was like a first year resident all over again.
In addition to the above, the location the program covers could be important. If you're in an inner city residency, you'll see several drug dependent patients of a sort (poor, unemployed, cocaine dependent, 13 year girl who is prostituting herself to pay for her crack). In a program in the middle of the mid-west, the patient profiles will highly vary and you'll see drug dependent patients of a different sort (farmer who cooks amphetamines and is dependent on them).
For that reason, IMHO, it's better to be in a program with a wide diversity of patients. You'll want a program that covers a large geographic area or one of high population density for that reason. In a program that covers an entire county, you'll see a much wider population diversity than one that is only covering a few blocks of a city.
The only way to find out is to ask the programs. Ask during the interviews, ask what type of patients they get, and how far an area they cover. Also bear in mind that programs will often want to sell themselves to applicants. For example, if ask that you are interested in seeing a diversity of patients, the program may respond "well we have a a large immigrant population" when in reality-- over 90% of their patients are Russian immigrants because the specific neck of where their hospital is located is in the heart of little Russia in a big city (And yes, some programs are like that). I'd hardly call that diversity.
You'll want to know the quality of the teaching. Asking residents who are able to answer freely is key here. Several programs will have residents answer, but only in the presence of an attending which will likely reduce the odds of getting an honest answer.
What program will leave you with the most opportunities? Again, depends on what you want to do. Most programs, at least at this point, will open the road to several fellowships. It's highly possible for even a poor resident to get into a name-brand fellowship. I know because some of the worst residents I've seen got interviews at places like Columbia, Johns Hopkins, Harvard, etc. What's going on here, IMHO (and someone correct me if I'm wrong) is that the pool of available applicants going into fellowships is smaller than other fields--leading to this effect. I actually had a buddy of mine who was a terrible resident, and I talked him out of going into fellowship. I flat out told him "we both know you're lazy. You really want to go into fellowship? You're going to graduate from your program because they tolerate bad residents. You really think you're going to do well at Johns Hopkins?" One of the worst residents I've known got into one of the most competitive fellowships. (Now that's a story that'll make your eyes roll, but I won't mention it more here.)
Competitive programs will certainly open a wider door to academic and research positions. They also, more likely than not, will be great programs. Again as I wrote before, be mindful that the name will not always match the quality of the program, and if you really know what you want and it's a niche, some of the non-famous programs will have name-brand people who are great teachers such as Marsha Linehan at U. of Washington.